## Understanding interactions among genetic algorithm parameters (1999)

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Venue: | in Foundations of Genetic Algorithms 5 |

Citations: | 24 - 3 self |

### BibTeX

@INPROCEEDINGS{Deb99understandinginteractions,

author = {Kalyanmoy Deb and Samir Agrawal},

title = {Understanding interactions among genetic algorithm parameters},

booktitle = {in Foundations of Genetic Algorithms 5},

year = {1999},

pages = {265--286},

publisher = {Morgan Kaufmann}

}

### OpenURL

### Abstract

Genetic algorithms (GAs) are multi-dimensional and stochastic search methods, involving complex interactions among their parameters. For last two decades, researchers have been trying to understand the mechanics of GA parameter interactions by using various techniques|careful `functional ' decomposition of parameter interactions, empirical studies, and Markov chain analysis. Although the complexities in these interactions are getting clearer with such analyses, it still remains an open question in the mind of a new-comer to the eld or to a GA-practitioner as to what values of GA parameters (such as population size, choice of GA operators, operator probabilities, and others) to use in an arbitrary problem. In this paper, we investigate the performance of simple tripartite GAs on a number of simple to complex test problems from a practical standpoint. Since in a real-world situation, the overall time to run a GA is more or less dominated by the time consumed by objective function evaluations, we compare di erent GAs for a xed number of function evaluations. Based on probability calculations and simulation results, it is observed that for solving simple problems (unimodal or small modality problems) the mutation operator plays an important role, although GAs with the crossover operator alone can also solve these problems. However, the two operators (when applied alone) have two di erent working zones for the population size. For complex problems involving massive multi-modality and misleadingness (deception), the crossover operator is the key search operator. Based on these studies, it is recommended that when in doubt, the use of the crossover operator with an adequate population size is a reliable approach.

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Citation Context ...ir pair-wise effect on GA's performance. These isolated studies are worthwhile and have provided useful guidelines for choosing GA parameters, such as population size (Goldberg, Deb, and Clark, 1992� =-=Harik et al., 1997-=-) and control maps for operator probabilities (Goldberg, Deb, and Thierens, 1992� Thierens and Goldberg, 1993). In order to observe theinteractions of various GA parameters, empirical studies have als... |

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Citation Context ...and Riolo, 1997). To study the dynamics of these interactions, more sophisticated stochastic models using Markov chains have also been developed and analyzed (Chakraborty, Deb, and Chakraborty, 1996� =-=Nix and Vose, 1992-=-� Suzuki, 1993� Vose, 1992). Based on these studies, the following salient observations can be made: 1. An optimal mutation probability is dependent on the representation being used (Tate and Smith, 1... |

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Citation Context ...uations 10000 1000 100 2 10 100 Population Size 500 1000 Figure 6: Number of function evaluations needed to nd the optimal string for the Onemax problem. be used to explain why micro-GA applications (=-=Krishnakumar, 1989-=-) do not perform well with very small populations (such as 2 or 3), whereas they perform well on simpler problems with population sizes 5 or more. The above two subsections suggest that GAs with mutat... |

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Citation Context ...s for choosing GA parameters, such as population size (Goldberg, Deb, and Clark, 1992; Harik et al., 1997) and control maps for operator probabilities (Goldberg, Deb, and Thierens, 1992; Thierens and =-=Goldberg, 1993-=-). In order to observe the interactions of various GA parameters, empirical studies have also been used (De Jong, 1975; Eshelman and Schaffer, 1993; Schaffer et al., 1989; Wu, Lindsay, and Riolo, 1997... |

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Citation Context ...ators, operator probabilities, representation of decision variables, and others) interact in a complex way. More importantly, their interactions are largely dependent on the function being optimized (=-=Hart and Belew, 1991-=-). Since these interactions are complex and a complete analysis of all their interactions is di cult to achieve, researchers have used di erent analysis tools. Some studies carefully isolated interact... |

25 |
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Citation Context ... study the dynamics of these interactions, more sophisticated stochastic models using Markov chains have also been developed and analyzed (Chakraborty, Deb, and Chakraborty, 1996� Nix and Vose, 1992� =-=Suzuki, 1993-=-� Vose, 1992). Based on these studies, the following salient observations can be made: 1. An optimal mutation probability is dependent on the representation being used (Tate and Smith, 1993). Similar ... |

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Citation Context ...1993� Scha er et al., 1989� Wu, Lindsay, and Riolo, 1997). To study the dynamics of these interactions, more sophisticated stochastic models using Markov chains have also been developed and analyzed (=-=Chakraborty, Deb, and Chakraborty, 1996-=-� Nix and Vose, 1992� Suzuki, 1993� Vose, 1992). Based on these studies, the following salient observations can be made: 1. An optimal mutation probability is dependent on the representation being use... |

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Citation Context ...operator to give importance to, from a practical standpoint. 3. Crossover is useful in problems where building block exchange is necessary (Eshelman and Scha er, 1993� Goldberg, Deb, and Clark, 1992, =-=Spears, 1993-=-). The use of mutation may destroy already-found good information and therefore may not be suitable in such problems. With this in mind, it is then suggested that GAs maywork well with a large crossov... |

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Citation Context ...for the crossover operator, where it is highlighted that an optimal operator is largely dependent on the underlying coding used to represent decision variables (Battle and Vose, 1990� Radcli e, 1991� =-=Kargupta, Deb, and Goldberg, 1992-=-). 2. The e ect of crossover and mutation can be interchanged by using a suitable coding transformation (Culberson, 1994). However, the study does not mention anything about the cost (in terms of func... |

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Citation Context ...s for choosing GA parameters, such as population size (Goldberg, Deb, and Clark, 1992� Harik et al., 1997) and control maps for operator probabilities (Goldberg, Deb, and Thierens, 1992� Thierens and =-=Goldberg, 1993-=-). In order to observe theinteractions of various GA parameters, empirical studies have also been used (De Jong, 1975� Eshelman and Scha er, 1993� Scha er et al., 1989� Wu, Lindsay, and Riolo, 1997). ... |

4 |
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Citation Context ...arbitrary problem, a great deal of e ort has been spent to use a exible representation scheme so that GAs can evolve an e cient representation on the y (Goldberg, Korb, and Deb, 1989� Kargupta, 1996� =-=Harik, 1997-=-). In this study, we do not address this so-called linkage problem and always use a tight representation scheme in solving all test problems. When such parametric studies are to be made, it is importa... |

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Citation Context ..._m=1.0/l 2 10 100 Population Size 500 1000 2000 Figure 10: The Unuse factor U for the four-peaked function. these GAs work the best. Similar performance trends are also observed by other researchers (=-=Oates and Corne, 1998-=-). Although the exact reason for peak performance at two distinct ranges of population sizes of mutation-based GAs is not studied here, it is conjectured that peak performance with smaller population ... |

2 |
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Citation Context ...1993). Similar arguments are also made for the crossover operator, where it is highlighted that an optimal operator is largely dependent on the underlying coding used to represent decision variables (=-=Battle and Vose, 1990-=-� Radcli e, 1991� Kargupta, Deb, and Goldberg, 1992). 2. The e ect of crossover and mutation can be interchanged by using a suitable coding transformation (Culberson, 1994). However, the study does no... |

2 |
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Citation Context ...be allowed more number of points to search from. Although there exists no clear study specifying what would cause GA-di culty, the following few factors have been suggested elsewhere (Goldberg, 1993� =-=Horn, Goldberg, and Deb, 1994-=-): 1. Multi-modality 2. Deception 3. Isolation 4. Collateral noise Multi-modality causes di culty toany search and optimization method, because of the presence of a number of false attractors. For som... |

2 |
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Citation Context ...true optimum in any run when the population size is more than 50. We now investigate why GAs did not perform well with very small populations. 3.1.2 Small populations It has been discussed elsewhere (=-=Mfihlenbein, 1992-=-) that for Onemax problems, the most difficult task is to move from strings having Hamming distances one to the optimal string. This is because the transition probability of this movement for a single... |

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1 |
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(Show Context)
Citation Context ...eb, and Thierens, 1992; Thierens and Goldberg, 1993). In order to observe the interactions of various GA parameters, empirical studies have also been used (De Jong, 1975; Eshelman and Schaffer, 1993; =-=Schaffer et al., 1989-=-; Wu, Lindsay, and Riolo, 1997). To study the dynamics of these interactions, more sophisticated stochastic models using Markov chains have also been developed and analyzed (Chakraborty, Deb, and Chak... |